Significant pair production (pair density \(>100n_c\) ) begins at \(t\simeq 7T_0\) , and this timing is also verified by the positron energy evolution in Fig. REF . The positron profile is shown in Fig. REF (b) at \(t=11.4T_0\) . The maximum positron density exceeds \(2000n_c\sim a_0n_c\) , consistent with previous studies [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. The energy spectra of the plasmas are shown in Fig. REF (c). Although the laser-plasma coupling is highly nonlinear, the spectra of pair species show thermal tails whose temperatures are \(\sim 200 \ \mathrm {MeV}\)  based on exponential fits. The system energy is well conserved [black lines in Fig. REF (a)]. The system energy drops after \(t\sim 20T_0\) , because the laser and energetic particles start to escape the simulation box. The laser coupling into the plasma (including the emitted photons and pair particles) saturates since \(t\sim 13T_0\) , indicating a higher coupling efficiency of \(66\%\)  in the QED simulation than in the non-QED one (just \( 47\%\) ). The higher coupling efficiency is due to the QED effects, i.e., photon emission and pair production whose energies make up \(\sim 44\%\)  and \(\sim 15\%\)  of the plasma energy, respectively. We pay special attention to the electric fields polarized in the (\(x,\ y\) ) plane [Fig. REF (b)]. For the laser-plasma configuration here, the ideally specular reflection is along \(+y\)  direction shown by the red arrow in Fig. REF (a). Therefore, \(E_x\)  is the main component of the reflected field, and its energy in the QED simulation is just \(74\%\)  of the non-QED simulation, also indicating the higher absorption (lower reflection) when the QED effects are enabled [1]}, [2]}, [5]}. Given that the laser is reflected along a wide range of directions due to the deformation of the target surface by laser's radiation pressure [10]}, the total electric energy (\(|E_x|^2+|E_y|^2\) ) is also examined. It shows that \(73\%\)  of the electric energy is absorbed by the plasma in the QED simulation, while only \(58\%\)  is absorbed in the non-QED simulation. The difference in laser absorption is further verified by the corresponding HHG spectrum shown below.
<FIGURE><FIGURE>